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Derivative of:
Derivative of f(x)=x^2
Derivative of (x+1)*(x+2)^2*(x+3)^3
Derivative of tan(x)-x^2
Derivative of tan(2*x)/(1-cot(2*x))
Integral of d{x}:
sinx/1+cos^2x
Identical expressions
sinx/ one +cos^2x
sinus of x divide by 1 plus co sinus of e of squared x
sinus of x divide by one plus co sinus of e of squared x
sinx/1+cos2x
sinx/1+cos²x
sinx/1+cos to the power of 2x
sinx divide by 1+cos^2x
Similar expressions
sinx/1-cos^2x

The derivative of the function/ sinx/1+cos^2x

Derivative of sinx/1+cos^2x

The solution

You have entered [src]

sin(x)      2   
------ + cos (x)
  1

$$\frac{\sin{\left(x \right)}}{1} + \cos^{2}{\left(x \right)}$$

sin(x)/1 + cos(x)^2

Detail solution

Differentiate $\frac{\sin{\left(x \right)}}{1} + \cos^{2}{\left(x \right)}$ term by term:
1. The derivative of a constant times a function is the constant times the derivative of the function.
  1. The derivative of sine is cosine:
    
    $\frac{d}{d x} \sin{\left(x \right)} = \cos{\left(x \right)}$
  So, the result is: $\cos{\left(x \right)}$
2. Let $u = \cos{\left(x \right)}$ .
3. Apply the power rule: $u^{2}$ goes to $2 u$
4. Then, apply the chain rule. Multiply by $\frac{d}{d x} \cos{\left(x \right)}$ :
  1. The derivative of cosine is negative sine:
    
    $\frac{d}{d x} \cos{\left(x \right)} = - \sin{\left(x \right)}$
  The result of the chain rule is:
  
  $- 2 \sin{\left(x \right)} \cos{\left(x \right)}$
The result is: $- 2 \sin{\left(x \right)} \cos{\left(x \right)} + \cos{\left(x \right)}$
Now simplify:

$- \sin{\left(2 x \right)} + \cos{\left(x \right)}$

The answer is:

$- \sin{\left(2 x \right)} + \cos{\left(x \right)}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

-2*cos(x)*sin(x) + cos(x)

$$- 2 \sin{\left(x \right)} \cos{\left(x \right)} + \cos{\left(x \right)}$$

Simplify

The second derivative [src]

               2           2   
-sin(x) - 2*cos (x) + 2*sin (x)

$$2 \sin^{2}{\left(x \right)} - \sin{\left(x \right)} - 2 \cos^{2}{\left(x \right)}$$

Simplify

The third derivative [src]

(-1 + 8*sin(x))*cos(x)

$$\left(8 \sin{\left(x \right)} - 1\right) \cos{\left(x \right)}$$

Simplify